Verizon is already under contract by the federal government on other HHS projects, but is not currently working on the health care site.

President Obama acknowledged Monday that the exchange rollout has not gone smoothly, and assured Americans that the government is working to fix glitches on the website.

"The website has been too slow, people have been getting stuck during the application process, and I think it's fair to say that nobody is more frustrated by that than I am, precisely because the product is good," Obama said in the White House Rose Garden. "We've had some of the best I.T. talent in the entire country join the team and we're well into a tech surge to fix the problem."

A new report found that the government went ahead with the website despite a failed test a few days prior to the launch date.